// certify that digraph is either acyclic or has a directed cycle
private boolean check() {
// edge-weighted digraph is cyclic
if (hasCycle()) {
// verify cycle
DirectedEdge first = null, last = null;
for (DirectedEdge e : cycle()) {
if (first == null) first = e;
if (last != null) {
if (last.to() != e.from()) {
System.err.printf("cycle edges %s and %s not incident\n", last, e);
return false;
}
}
last = e;
}
if (last.to() != first.from()) {
System.err.printf("cycle edges %s and %s not incident\n", last, first);
return false;
}
}
return true;
}
// relax edge e, but update if you find a *longer* path
private void relax(DirectedEdge e) {
int v = e.from(), w = e.to();
if (distTo[w] < distTo[v] + e.weight()) {
distTo[w] = distTo[v] + e.weight();
edgeTo[w] = e;
}
}
/**
* Reads the currency exchange table from standard input and
* prints an arbitrage opportunity to standard output (if one exists).
*
* @param args the command-line arguments
*/
public static void main(String[] args) {
// V currencies
int V = StdIn.readInt();
String[] name = new String[V];
// create complete network
EdgeWeightedDigraph G = new EdgeWeightedDigraph(V);
for (int v = 0; v < V; v++) {
name[v] = StdIn.readString();
for (int w = 0; w < V; w++) {
double rate = StdIn.readDouble();
DirectedEdge e = new DirectedEdge(v, w, -Math.log(rate));
G.addEdge(e);
}
}
// find negative cycle
BellmanFordSP spt = new BellmanFordSP(G, 0);
if (spt.hasNegativeCycle()) {
double stake = 1000.0;
for (DirectedEdge e : spt.negativeCycle()) {
StdOut.printf("%10.5f %s ", stake, name[e.from()]);
stake *= Math.exp(-e.weight());
StdOut.printf("= %10.5f %s\n", stake, name[e.to()]);
}
}
else {
StdOut.println("No arbitrage opportunity");
}
}
// check optimality conditions: either
// (i) there exists a negative cycle reacheable from s
// or
// (ii) for all edges e = v->w: distTo[w] <= distTo[v] + e.weight()
// (ii') for all edges e = v->w on the SPT: distTo[w] == distTo[v] + e.weight()
private boolean check(EdgeWeightedDigraph G, int s) {
// has a negative cycle
if (hasNegativeCycle()) {
double weight = 0.0;
for (DirectedEdge e : negativeCycle()) {
weight += e.weight();
}
if (weight >= 0.0) {
System.err.println("error: weight of negative cycle = " + weight);
return false;
}
}
// no negative cycle reachable from source
else {
// check that distTo[v] and edgeTo[v] are consistent
if (distTo[s] != 0.0 || edgeTo[s] != null) {
System.err.println("distanceTo[s] and edgeTo[s] inconsistent");
return false;
}
for (int v = 0; v < G.V(); v++) {
if (v == s) continue;
if (edgeTo[v] == null && distTo[v] != Double.POSITIVE_INFINITY) {
System.err.println("distTo[] and edgeTo[] inconsistent");
return false;
}
}
// check that all edges e = v->w satisfy distTo[w] <= distTo[v] + e.weight()
for (int v = 0; v < G.V(); v++) {
for (DirectedEdge e : G.adj(v)) {
int w = e.to();
if (distTo[v] + e.weight() < distTo[w]) {
System.err.println("edge " + e + " not relaxed");
return false;
}
}
}
// check that all edges e = v->w on SPT satisfy distTo[w] == distTo[v] + e.weight()
for (int w = 0; w < G.V(); w++) {
if (edgeTo[w] == null) continue;
DirectedEdge e = edgeTo[w];
int v = e.from();
if (w != e.to()) return false;
if (distTo[v] + e.weight() != distTo[w]) {
System.err.println("edge " + e + " on shortest path not tight");
return false;
}
}
}
StdOut.println("Satisfies optimality conditions");
StdOut.println();
return true;
}
/**
* Adds the directed edge {@code e} to this edge-weighted digraph.
*
* @param e the edge
* @throws IllegalArgumentException unless endpoints of edge are between {@code 0}
* and {@code V-1}
*/
public void addEdge(DirectedEdge e) {
int v = e.from();
int w = e.to();
validateVertex(v);
validateVertex(w);
adj[v].add(e);
indegree[w]++;
E++;
}
// relax edge e and update pq if changed
private void relax(DirectedEdge e) {
int v = e.from(), w = e.to();
if (distTo[w] > distTo[v] + e.weight()) {
distTo[w] = distTo[v] + e.weight();
edgeTo[w] = e;
if (pq.contains(w)) pq.decreaseKey(w, distTo[w]);
else pq.insert(w, distTo[w]);
}
}
/**
* Adds the directed edge {@code e} to the edge-weighted digraph (if there
* is not already an edge with the same endpoints).
* @param e the edge
*/
public void addEdge(DirectedEdge e) {
int v = e.from();
int w = e.to();
validateVertex(v);
validateVertex(w);
if (adj[v][w] == null) {
E++;
adj[v][w] = e;
}
}
// check optimality conditions:
// (i) for all edges e: distTo[e.to()] <= distTo[e.from()] + e.weight()
// (ii) for all edge e on the SPT: distTo[e.to()] == distTo[e.from()] + e.weight()
private boolean check(EdgeWeightedDigraph G, int s) {
// check that edge weights are nonnegative
for (DirectedEdge e : G.edges()) {
if (e.weight() < 0) {
System.err.println("negative edge weight detected");
return false;
}
}
// check that distTo[v] and edgeTo[v] are consistent
if (distTo[s] != 0.0 || edgeTo[s] != null) {
System.err.println("distTo[s] and edgeTo[s] inconsistent");
return false;
}
for (int v = 0; v < G.V(); v++) {
if (v == s) continue;
if (edgeTo[v] == null && distTo[v] != Double.POSITIVE_INFINITY) {
System.err.println("distTo[] and edgeTo[] inconsistent");
return false;
}
}
// check that all edges e = v->w satisfy distTo[w] <= distTo[v] + e.weight()
for (int v = 0; v < G.V(); v++) {
for (DirectedEdge e : G.adj(v)) {
int w = e.to();
if (distTo[v] + e.weight() < distTo[w]) {
System.err.println("edge " + e + " not relaxed");
return false;
}
}
}
// check that all edges e = v->w on SPT satisfy distTo[w] == distTo[v] + e.weight()
for (int w = 0; w < G.V(); w++) {
if (edgeTo[w] == null) continue;
DirectedEdge e = edgeTo[w];
int v = e.from();
if (w != e.to()) return false;
if (distTo[v] + e.weight() != distTo[w]) {
System.err.println("edge " + e + " on shortest path not tight");
return false;
}
}
return true;
}
